This year when I started balanced forces with the hover disc FBD’s (see here for the general idea), I decided to try connected forces and motion more explicitly.

First, I turned on the hover disc and pushed it across the circle and then asked the student to push it back to me faster. I asked students to sketch what they think the velocity graph would look like for this motion. Then they compared with their neighbor, and I chose 3 students to sketch their velocity graphs on the board. I chose the following 3 graphs because they were all a little different.

We talked about the similarities between the graphs (all have positive and negative portion, all cross over the time-axis -well maybe not the blue one). And differences (green and blue have constant velocity portions and the red one doesn’t. The red and green one take time to speed up and slow down. The green one shoes the second speed as greater but the blue and red show the speeds as equal).

Then we used the motion detector to check our predictions.

Students noticed some cool things on this graph – the second portion has a greater speed, and it also takes less time to cross the circle (same distance). This is a nice precursor to thinking about the area under the v-t graph.

Then we turned the hover disc off and I pushed it. Students made graph predictions again, and I selected 3 different ones to sketch on the board.

Again, talk about similarities and differences and then check with motion detector:

After doing this series of graphs, I asked students to think about why the motion was different when the hover disc was turned on vs. turned off. Ultimately we want them to connect constant velocity with balanced forces and changing velocity with unbalanced forces.

Most students talked about the air from the hover disc reducing friction, but of course there were some students thinking that the hover disc has something that propels it forward when it’s turned on. (like a Roomba!) I asked how we could test this, and they said let’s turn it on and set it down on the floor without pushing it. If it doesn’t move, there’s no force propelling it forward. Any guesses as to what happened when we did this? This thing always moves when you set it down. Some said “well the floor’s not perfectly flat!” but that wouldn’t be very convincing to me if I thought it was self-propelling. I suppose we would try setting it down many many times, always with the same starting orientation, to see if it always moves in the same direction, but we didn’t do that.

So the question is – how do students come to understand that there are zero horizontal forces in the first situation? It is hard to prove this empirically. It usually ends with me just telling them this is true, which feels unsatisfying to me.

I do tell them it took a long time for scientists to sort this out, and in a subsequent class I showed them Galileo’s argument in response to the Aristotelian view. A ball rolled down a ramp will continue to roll at a constant speed forever, unless there is some force that acts on it to speed it up or slow it down.

I didn’t explicitly ask students to come up with counterarguments (as David Hammer did in the physics class he taught, described in his Misconceptions vs. P-Prims paper). But, one student did this spontaneously: “If I’m playing devil’s advocate, I can believe the ball would go on forever, but that doesn’t convince me that there’s no force causing it to do that. Wouldn’t Aristotle say the ball must have some sort of internal force to make it keep moving forever?” We (the other students and I) didn’t have a very satisfying response to that. Do you?